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A generalization of Eichler's trace formula.

Juliusz Brzezinski (1997)

Collectanea Mathematica

Eichler's trace formula for traces of the Brandt-Eichler matrices is proved for arbitrary totally definite orders in central simple algebras of prime index over global fields. A formula for type numbers of such orders is proved as an application.

A Generalization of Kummer's Criterion.

Ralph Greenberg (1973)

Inventiones mathematicae

A generalization of Maillet and Demyanenko determinants

Mikihito Hirabayashi (1998)

Acta Arithmetica

A generalization of Scholz’s reciprocity law

Mark Budden, Jeremiah Eisenmenger, Jonathan Kish (2007)

Journal de Théorie des Nombres de Bordeaux

We provide a generalization of Scholz’s reciprocity law using the subfields $K_{2^{t - 1}}$ and $K_{2^{t}}$ of $ℚ (ζ_{p})$ , of degrees $2^{t - 1}$ and $2^{t}$ over $ℚ$ , respectively. The proof requires a particular choice of primitive element for $K_{2^{t}}$ over $K_{2^{t - 1}}$ and is based upon the splitting of the cyclotomic polynomial $Φ_{p} (x)$ over the subfields.

A generalization of the Chowla-Selberg formula.

Y. Nakkajima, Y. Taguchi (1991)

Journal für die reine und angewandte Mathematik

A generalization of the Lerch-Mordell formulas for positive discriminants

Jerzy Urbanowicz (1990)

Colloquium Mathematicae

A generalization of the sizes of differential equations and its applications to $G$ -function theory

Makoto Nagata (2001)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

A generalization of Voronoï’s Theorem to algebraic lattices

Kenji Okuda, Syouji Yano (2010)

Journal de Théorie des Nombres de Bordeaux

Let $K$ be an algebraic number field and $𝒪_{K}$ the ring of integers of $K$ . In this paper, we prove an analogue of Voronoï’s theorem for $𝒪_{K}$ -lattices and the finiteness of the number of similar isometry classes of perfect $𝒪_{K}$ -lattices.